So right now, iirc, there's an issue with antisocial dwarves, they have a broad but shallow relationship pool because they seek places to socialise, but no specific dwarves to socialise with, leading to low marriage rates and an overdependence on migrants to keep population up, as well as poor mood due to a lack of friends to have pleasant conversation with, and lack of weddings and children to boost mood too, though if a marriage does manage to happen then there is certainly no shortage of children for that couple. I have a couple of suggestions to remedy this:
1) Dwarves make plans with friends and hang out
together when they feel the need for some social interaction, friends who are also feeling that need, or who aren't really doing anything anyway, agree to meet up for an activity (they don't necessarily have to meet up to plan, they could use whatever dwarven telepathy they use to take orders from the player/nobles). They all go to the same meeting area/location, stay close enough to each other that each member of the group can talk to at least one other group member, and they perform appropriate activities for the zone, be it drunken revelry, admiration of art, or a group study. This should be restricted to dwarves that are already friends, and group sizes should stay fairly small to keep it distinguishable from parties, maybe a maximum of 8 so that if they go to the tavern or the library they can all sit around the same table.
1a) A dwarf who has no friends in their current burrow who feels the need for some social interaction seeks friends among some of their acquaintances, these interactions may end in drunken fistfights if they end up having grudges rather than friendships, but hey then they might get a little more focus after causing trouble/fighting/arguing as well as the conversation prior to the violence sating their need for social interaction.
2) Sexually compatible and available acquaintances (not friends since if they were gonna be lovers they would be already), and already existing couples, go on dates if both of them feel the need for romance. Dating acquaintances may also result in a brawl if they end up with a grudge since they're only acquaintances, but you can RP it as the dwarven equivalent of getting slapped for saying/doing something the other person strongly disagrees with. Dates would basically work just like friends meeting up, with the exception that only 2 dwarves may be on the same date.
Hopefully, both should make dwarves happier and more sociable, 1 should get them to form cliques, which could be expanded into gangs during the crime arc or something if the game can be made to recognise these cliques somehow, and 2 should make them less prone to extinction through celibacy.
EDIT: Thread was a bit longer than I anticipated, so I'm gonna list as many related suggestions that popped up during the discussion here as I can find (not including those mentioned in the OP) to make it easier for people to get involved and add their own ideas and opinions, or to pique interest into reading the thread since I'm just doing quick 1 sentence summaries of the suggestions.
Friends seeking other friends out for a chat without interrupting jobs.
Increase interaction radius and allow for interaction during jobs.
Sitting at adjacent tables forcing conversation.
Non-dining rec room, for more personal interactions that are best kept away from the drunken revelry/violence of the tavern.
Increased interaction between neighbours.
Friends moving their bedrooms to be closer together.
Rivals moving their bedrooms to be further away from each other.
Low-privacy friends visiting each other's rooms. (contested, some concerns about compatibility with future oxygen/light simulation)
High-privacy, low-gregariousness dwarves getting annoyed by frequent social interaction, minor bad thought.
Park/nature reserve zones, residents and visitors that value nature can take walks in the park/nature reserve, or go for a picnic, can bring friends and chat during the walk/picnic.
Ceremonies, followed by food, drink, and socialising. Provides a reason to assign temple performers if religious holidays also happen.
Mockery based on the comedian skill, may cause a variety of responses from the subject of the mockery, depending on personality, possible brawl trigger, may need associated ethics and crimes for things like harassment.
Non-mutual relationships. (e.g. one-sided relationship boosts for watching/listening to high quality performances, being helped when in need, e.c.t.)
Playdates, so dwarven children make friends with each other, and babysitting, so that they form connections with adults other than their parents
If/when religious traditions happen, breach of doctrine and seeking absolution could affect relations with fellow worshippers, absolution may be refused if the priest has poor relations with the sinner, resulting in bad thoughts.
If games can have spectators, non-mutual relationships could allow for fans, who could develop some level of rivalry with fans of other contestants/teams, especially if contestants/teams can be accused of foul play, could be especially interesting if sports are included as games.
Dwarves that have grudges can challenge each other to duels/combat sports, or less organised and more legally dubious fights
Dwarves having opinions on professions perhaps leading to elitism